Non-singular method of fundamental solutions for elasticity problems in three-dimensions

2018 ◽  
Vol 96 ◽  
pp. 23-35 ◽  
Author(s):  
Q.G. Liu ◽  
B. Šarler
Keyword(s):  
Fundamental Solutions ◽  
Three Dimensions ◽  
Method Of Fundamental Solutions ◽  
Elasticity Problems

A Moving Pseudo-Boundary MFS for Three-Dimensional Void Detection

2013 ◽  
Vol 5 (04) ◽  
pp. 510-527 ◽  
Author(s):  
Andreas Karageorghis ◽  
Daniel Lesnic ◽  
Liviu Marin
Keyword(s):  
Three Dimensional ◽  
Nonlinear Least Squares ◽  
Fundamental Solutions ◽  
Cauchy Data ◽  
Three Dimensions ◽  
Method Of Fundamental Solutions ◽  
Void Detection ◽  
Spherical Parametrization ◽  
Least Squares Minimization

AbstractWe propose a new moving pseudo-boundary method of fundamental solutions (MFS) for the determination of the boundary of a three-dimensional void (rigid inclusion or cavity) within a conducting homogeneous host medium from overdetermined Cauchy data on the accessible exterior boundary. The algorithm for imaging the interior of the medium also makes use of radial spherical parametrization of the unknown star-shaped void and its centre in three dimensions. We also include the contraction and dilation factors in selecting the fictitious surfaces where the MFS sources are to be positioned in the set of unknowns in the resulting regularized nonlinear least-squares minimization. The feasibility of this new method is illustrated in several numerical examples.

scholarly journals The Method of Fundamental Solutions for Three-Dimensional Nonlinear Free Surface Flows Using the Iterative Scheme

2019 ◽  
Vol 9 (8) ◽  
pp. 1715 ◽  
Author(s):  
Cheng-Yu Ku ◽  
Jing-En Xiao ◽  
Chih-Yu Liu
Keyword(s):  
Free Surface ◽  
Nonlinear Boundary ◽  
Three Dimensional ◽  
Nonlinear Boundary Conditions ◽  
Fundamental Solutions ◽  
Free Surface Flows ◽  
Three Dimensions ◽  
Method Of Fundamental Solutions ◽  
Surface Flows ◽  
Nonlinear Free Surface

In this article, we present a meshless method based on the method of fundamental solutions (MFS) capable of solving free surface flow in three dimensions. Since the basis function of the MFS satisfies the governing equation, the advantage of the MFS is that only the problem boundary needs to be placed in the collocation points. For solving the three-dimensional free surface with nonlinear boundary conditions, the relaxation method in conjunction with the MFS is used, in which the three-dimensional free surface is iterated as a movable boundary until the nonlinear boundary conditions are satisfied. The proposed method is verified and application examples are conducted. Comparing results with those from other methods shows that the method is robust and provides high accuracy and reliability. The effectiveness and ease of use for solving nonlinear free surface flows in three dimensions are also revealed.

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